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Answer :
Final answer
The next time all the lights will flash together is after 20 seconds because it is the least common multiple (LCM) of their individual flashing intervals: 1 second for white, 4 seconds for green, and 5 seconds for blue. This ensures that they sync up at the 20-second mark.
Correct answer is (option C)
Explanation
To determine when the white, green, and blue lights will all flash together, we need to find the least common multiple (LCM) of the flashing intervals for each light.
The white light flashes every second, which means it has a flashing interval of 1 second.
The green light flashes every 4th flash, which means its interval is 4 seconds.
The blue light flashes every 5th flash, which means its interval is 5 seconds.
To find the LCM of these intervals, we can use the prime factorization method:
The prime factorization of 1 is 1.
The prime factorization of 4 is [tex]2^2[/tex].
The prime factorization of 5 is 5.
Now, we take the highest power of each prime factor:
LCM = [tex]2^2[/tex] * 5 = 4 * 5 = 20
So, the lights will all flash together at every 20-second interval. Therefore, the next time they will all flash together is after 20 seconds, making the correct answer C) After 20 seconds.
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